A multiscale model for anisotropic damage and hysteresis in biodegradable polymers

A multiscale model for anisotropic damage and hysteresis in biodegradable polymers

Vitucci Gennaro, De Tommasi Domenico, Di Stefano Salvatore, Puglisi Giuseppe, Trentadue Francesco

Abstract. Predicting the mechanical response of biological soft materials requires an understanding of the complex phenomena characterizing their microscale. In this work, we use an existing versatile framework, based on assumptions on the statistical distribution of biolpolymers at the network scale, for extending our previous entropic constitutive model of Worm-Like Chains networks to different deformation classes. Furthermore, we include the effect of molecules topological constraints by introducing an energy term depending on the second invariant of the Green-Cauchy tensor. In this way we are able to qualitatively reproduce, with a limited set of physically meaningful constitutive parameters, a range of observed phenomena such as induced anisotropy, stress softening, hardening, Mullins effect, evolution of permanent stretches.

Keywords
Mullins Effect, Multiscale Models, Microsphere Approach, Biodegradable Polymers

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Vitucci Gennaro, De Tommasi Domenico, Di Stefano Salvatore, Puglisi Giuseppe, Trentadue Francesco, A multiscale model for anisotropic damage and hysteresis in biodegradable polymers, Materials Research Proceedings, Vol. 26, pp 41-46, 2023

DOI: https://doi.org/10.21741/9781644902431-7

The article was published as article 7 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] F. Trentadue, D. De Tommasi, and G. Puglisi, “A predictive micromechanically-based model for damage and permanent deformations in copolymer sutures,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 115, p. 104277, 2021. https://doi.org/10.1016/j.jmbbm.2020.104277
[2] D. De Tommasi, N. Millardi, G. Puglisi, and G. Saccomandi, “An energetic model for macromolecules unfolding in stretching experiments,” Journal of The Royal Society Interface, vol. 10, no. 88, p. 20130651, 2013. https://doi.org/10.1098/rsif.2013.0651
[3] S. Goektepe and C. Miehe, “A micro–macro approach to rubber-like materials. part iii: The micro-sphere model of anisotropic mullins-type damage,” Journal of the Mechanics and Physics of Solids, vol. 53, no. 10, pp. 2259–2283, 2005. https://doi.org/10.1016/j.jmps.2005.04.010
[4] G. Vitucci, D. De Tommasi, G. Puglisi, and F. Trentadue, “A predictive microstructure-based approach for the anisotropic damage, residual stretches and hysteresis in biodegradable sutures,” arXiv preprint arXiv:2206.00345, 2022. https://doi.org/10.1021/ma00130a008
[5] J. F. Marko and E. D. Siggia, “Stretching dna,” Macromolecules, vol. 28, no. 26, pp. 8759–8770, 1995.
[6] M. Rubinstein, R. H. Colby, et al., Polymer physics, vol. 23. Oxford university press New York, 2003.
[7] W. Kuhn and F. Gr¨un, “Beziehungen zwischen elastischen konstanten und dehnungsdoppelbrechung hochelastischer stoffe,” Kolloid-Zeitschrift, vol. 101, no. 3, pp. 248–271, 1942. https://doi.org/10.1007/BF01793684
[8] G. Bertotti, Hysteresis in magnetism: for physicists, materials scientists, and engineers. Gulf Professional Publishing, 1998.
[9] M. Doi, S. F. Edwards, and S. F. Edwards, The theory of polymer dynamics, vol. 73. oxford university press, 1988.
[10] R. W. Ogden, Non-linear elastic deformations. Courier Corporation, 1997.
[11] P. Baˇzant and B. Oh, “Efficient numerical integration on the surface of a sphere,” ZAMMJournal of Applied Mathematics and Mechanics/Zeitschrift f¨ur Angewandte Mathematik und Mechanik, vol. 66, no. 1, pp. 37–49, 1986. https://doi.org/10.1002/zamm.19860660108
[12] C. O. Horgan and G. Saccomandi, “Constitutive modelling of rubber-like and biological materials with limiting chain extensibility,” Mathematics and mechanics of solids, vol. 7, no. 4, pp. 353–371, 2002. https://doi.org/10.1177/108128028477
[13] M. Destrade, J. G. Murphy, and G. Saccomandi, “Simple shear is not so simple,” International Journal of Non-Linear Mechanics, vol. 47, no. 2, pp. 210–214, 2012. https://doi.org/10.1016/j.ijnonlinmec.2011.05.008
[14] B. Yohsuke, K. Urayama, T. Takigawa, and K. Ito, “Biaxial strain testing of extremely soft polymer gels,” Soft Matter, vol. 7, no. 6, pp. 2632–2638, 2011. https://doi.org/10.1039/c0sm00955e
[15] V. Gennaro, I. Argatov, and G. Mishuris. “An asymptotic model for the deformation of a transversely isotropic, transversely homogeneous biphasic cartilage layer.” Mathematical Methods in the Applied Sciences 40.9 (2017): 3333-3347. https://doi.org/10.1002/mma.3895
[16] G. Vitucci and G. Mishuris. “Three-dimensional contact of transversely isotropic transversely homogeneous cartilage layers: a closed-form solution.” European Journal of Mechanics-A/Solids 65 (2017): 195-204. https://doi.org/10.1016/j.euromechsol.2017.04.004